P ARADOXES IN F AIR M ACHINE L EARNING Paul Glz, Anson Kahng, and - - PowerPoint PPT Presentation

PARADOXES IN FAIR MACHINE LEARNING

Paul Gölz, Anson Kahng, and Ariel Procaccia

NeurIPS 2019

RESEARCH QUESTION

What is the relationship between 
 fairness in machine learning and fairness in fair division?

RESEARCH QUESTION

What is the relationship between 
 fairness in machine learning and fairness in fair division?

Statistical notions of fairness (e.g., equalized odds) Axioms of fair division (e.g., resource monotonicity, population monotonicity)

RESEARCH QUESTION

What is the relationship between 
 fairness in machine learning and fairness in fair division?

Statistical notions of fairness (e.g., equalized odds) Axioms of fair division (e.g., resource monotonicity, population monotonicity)

In order to compare these, we need the right setting.

CLASSIFICATION WITH CARDINALITY CONSTRAINTS

Classification problem with a fixed budget of available resources to distribute: e.g., financial aid. Goal: maximize efficiency (fraction of loans repaid)

Loans Applicants Two groups: hats and no hats

CLASSIFICATION WITH CARDINALITY CONSTRAINTS

Loans Applicants Two groups: hats and no hats

As a classification problem: label k applicants positively As a fair division problem: divide k loans among applicants What does it mean to be fair in each setting?

FAIR DIVISION AXIOMS

FAIRNESS CONCEPTS

Research question (rephrased): 
 How much does efficiency suffer if we must satisfy both equalized odds and various fair division axioms? Equalized odds Demographic parity Resource monotonicity Population monotonicity Consistency

STATISTICAL FAIRNESS

STATISTICAL FAIRNESS

Equalized Odds (EO): “A predictor satisfies equalized odds with respect to a protected attribute and outcome if and are independent conditional on .” (Hardt et al. 2016)

• ̂

Y A Y ̂ Y A Y Pr( ̂ Y = 1|A = 1, Y = 1) = Pr( ̂ Y = 1|A = 0, Y = 1) Pr( ̂ Y = 1|A = 1, Y = 0) = Pr( ̂ Y = 1|A = 0, Y = 0)

“True positive and false positive rates are equal across groups”

Equalized Odds (EO): “A predictor satisfies equalized odds with respect to a protected attribute and outcome if and are independent conditional on .” (Hardt et al. 2016)

• ̂

Y A Y ̂ Y A Y Pr( ̂ Y = 1|A = 1, Y = 1) = Pr( ̂ Y = 1|A = 0, Y = 1) Pr( ̂ Y = 1|A = 1, Y = 0) = Pr( ̂ Y = 1|A = 0, Y = 0)

STATISTICAL FAIRNESS

“True positive and false positive rates are equal across groups”

FAIR DIVISION AXIOMS

Resource monotonicity: “Adding more resources makes everyone better off.” Population monotonicity: “Adding more people makes everyone worse off.” Think of these axioms as preclusions of paradoxes.

RESOURCE MONOTONICITY

Budget Allocations

“Adding more resources makes everyone weakly better off”

If the school gets more money, no one gets less allocated to them.

$10 $15 $1 $1.1 $1.5 $2 $2.5 $3 $2 $3 $4 $4.9

POPULATION MONOTONICITY

Budget Allocations

“Adding more people makes everyone weakly worse off”

If someone turns down aid, this can’t hurt anyone else’s allocation.

$1 $0.9 $2 $3 $4 $1.5 $1.6 $2.8 $3.2 $10 $10

RESULTS (PARTIAL LIST)

• 1. In the cardinality-constrained model, we characterize

the optimal allocation rule that satisfies equalized odds

• 2. Equalized odds and resource monotonicity are

achievable with no loss to optimal EO efficiency

• 3. Any rule that satisfies equalized odds and population

monotonicity cannot achieve a constant-factor approximation to optimal EO efficiency

RESULTS (PARTIAL LIST)

• 1. In the cardinality-constrained model, we characterize

the optimal allocation rule that satisfies equalized odds

• 2. Equalized odds and resource monotonicity are

achievable with no loss to optimal EO efficiency

• 3. Any rule that satisfies equalized odds and population

monotonicity cannot achieve a constant-factor approximation to optimal EO efficiency 
 Thank you! Please come find me at poster #83.